I am working on a project in iOS and would like to enable key repeat. I have done quite a bit of looking around and have failed to come up with any option like that (which surprises me quite a bit, actually).

The other answers here are inaccurate. The correct answer is "sort of"

@MichaelGoerz Comment is correct. There seems to be a bug in iOS where key repeat only works for certain keys instead of all keys as expected. For example backspace will repeat per your settings but "w" won't. I recommend filing a bug report with Apple at https://bugreport.apple.com in an effort to prod them to fix this. This bug is highly irritating especially when using remote desktop tools where holding down a key might be required.

I occurred to me that this may also be by design, an attempt by Apple to be "helpful" by only allowing the most commonly used repeating keys. Due to the fact that the Settings->General->Accessibility->Keyboard->Key Repeat menu makes no mention of this I am treating it as a bug.

iPads don't have this problem when using an "official" Apple ("folio") keyboard. It's only broken when using a Bluetooth keyboard (I have both keyboard types at the moment for test purposes). So it's probably just another scenario where Apple is intentionally crippling non-apple products in order to make their own stuff look better and drive people the "official" accessories. Though, I suppose it could just be a bug when in Bluetooth mode. Not one that they will likely fix, however...
– TroyMar 17 at 12:45

I wanted to create a single line across the page On iPad. I went to Settings->General->Accessibility->Keyboard->Text Replacement. There you can add a keyboard shortcut for complete phrase. I created a shortcut consisting of a double tap of the underscore key to create a complete line of underscore keystrokes.